Enhancing Particle Filtering using Gaussian Processes

Imbiriba, Tales; Closas, Pau

doi:10.23919/fusion45008.2020.9190631

Cited by 6 publications

(5 citation statements)

References 16 publications

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“…Imbiriba et al proposed a GP-based sampling methodology in the context of particle filtering where, at each iteration, the GP's mean function was used to approximate the posterior distributions of particle filters and in the resampling process [26]. To adopt this strategy to the problem at hand we need to choose an appropriate model for the probability density function (PDF) to update.…”

Section: Adaptive Gp Random Samplingmentioning

confidence: 99%

“…Another alternative sampling algorithm might be considered where the balance between exploration and exploitation depends exclusively on the shape of the GP mean modeled as a probability density function (pdf). For instance, Imbiriba et al proposed a GP-based sampling algorithm developed in the context of particle filtering, where samples were drawn from a GP mean function that was normalized in order to make it a viable pdf [26]. This strategy presents some features that fit well with TMS mapping.…”

Section: Introductionmentioning

confidence: 99%

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Efficient TMS-Based Motor Cortex Mapping Using Gaussian Process Active Learning

Faghihpirayesh

Yarossi

Imbiriba

et al. 2021

IEEE Trans. Neural Syst. Rehabil. Eng.

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Transcranial Magnetic Stimulation (TMS) can be used to map cortical motor topography by spatially sampling the sensorimotor cortex while recording Motor Evoked Potentials (MEP) with surface electromyography (EMG). Traditional sampling strategies are time-consuming and inefficient, as they ignore the fact that responsive sites are typically sparse and highly spatially correlated. An alternative approach, commonly employed when TMS mapping is used for presurgical planning, is to leverage the expertise of the coil operator to use MEPs elicited by previous stimuli as feedback to decide which loci to stimulate next. In this paper, we propose to automatically infer optimal future stimulus loci using active learning Gaussian Process-based sampling in place of user expertise. We first compare the user-guided (USRG) method to the traditional grid selection method and randomized sampling to verify that the USRG approach has superior performance. We then compare several novel active Gaussian Process (GP) strategies with the USRG approach. Experimental results using real data show that, as expected, the USRG method is superior to the grid and random approach in both time efficiency and MEP map accuracy. We also found that an active warped GP entropy and a GP random-based strategy performed equally as well as, or even better than, the USRG method. These methods were completely automatic, and succeeded in efficiently sampling the regions in which the MEP response variations are largely confined. This work provides the foundation for highly efficient, fully automatized TMS mapping, especially when considered in the context of advances in robotic coil operation.

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Section: Adaptive Gp Random Samplingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficient TMS-Based Motor Cortex Mapping Using Gaussian Process Active Learning

Faghihpirayesh

Yarossi

Imbiriba

et al. 2021

IEEE Trans. Neural Syst. Rehabil. Eng.

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“…One drawback of particle filters is the high number of particles needed to accurately represent distributions. This issue is profoundly aggravated if the state-space dimension is large, making this filtering strategy unfeasible in such scenarios [10].…”

Section: A Cubature Kalman Filtermentioning

confidence: 99%

“…where q 4 is a feed-forward neural network with parameters ω, while equations ( 7), ( 8) and ( 10) are used for the dynamics of pressures P 1 , P 2 and P 5 . Note that equations ( 7)- (10) have recursive relations that become apparent when time is discretized:…”

Section: Application To the Retinal Circulationmentioning

confidence: 99%

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Cubature Kalman Filter Based Training of Hybrid Differential Equation Recurrent Neural Network Physiological Dynamic Models

Demirkaya¹,

Imbiriba²,

Lockwood³

et al. 2021

Preprint

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Modeling biological dynamical systems is challenging due to the interdependence of different system components, some of which are not fully understood. To fill existing gaps in our ability to mechanistically model physiological systems, we propose to combine neural networks with physicsbased models. Specifically, we demonstrate how we can approximate missing ordinary differential equations (ODEs) coupled with known ODEs using Bayesian filtering techniques to train the model parameters and simultaneously estimate dynamic state variables. As a study case we leverage a well-understood model for blood circulation in the human retina and replace one of its core ODEs with a neural network approximation, representing the case where we have incomplete knowledge of the physiological state dynamics. Results demonstrate that state dynamics corresponding to the missing ODEs can be approximated well using a neural network trained using a recursive Bayesian filtering approach in a fashion coupled with the known state dynamic differential equations. This demonstrates that dynamics and impact of missing state variables can be captured through joint state estimation and model parameter estimation within a recursive Bayesian state estimation (RBSE) framework.Results also indicate that this RBSE approach to training the NN parameters yields better outcomes (measurement/state estimation accuracy) than training the neural network with backpropagation through time in the same setting.

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